Introduction: Angles that can be parts of a triangle can be classified in three different ways. We show and define these types of angles. We assume the facts that the three angles in a triangle as well as any angles that form a straight line have a sum of 180º. Also a “square corner” has a measure of 90º.

The Lesson:

Angles are named and measured according to certain standards. An angle is formed when two lines or rays intersect. Examples and comments about the name and measure of the angle are shown below.

In example 1, we can name this angle A or . There is only one angle. Its measurement can be determined by using a protractor. But clearly the measure is less than 90º since this is not as wide an angle as a right angle or square corner.

In example 2, there are several angles formed and they must be named carefully to avoid confusion. We can name by the three letters B, P, and C making sure that the vertex P is the middle letter: We see that . Similarly . Together, angles 1 and 2 form which is clearly larger than a square corner; therefore its measure will be larger than 90º.

The angles in a triangle are all between in measure. We classify angles into three types as follows:

In the diagram below, suppose has a measure of 128º and has a measure of 80º. What is the measure of ?

Therefore

We subtract 80 and get

Note that we say “an angle CPD has a measure of 48” while we say . Whether or not we use the degree symbol depends on the context and usually upon whether the word “measure” is used. This varies depending on different textbooks as well.

Example Group #1

In the diagram above suppose the measures of and are 79º and 49º. Describe .